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Concept

Stationary process

Related publications (31)

Gaussian and sparse processes are limits of generalized Poisson processes

Michaël Unser, Julien René Fageot, Virginie Sophie Uhlmann

The theory of sparse stochastic processes offers a broad class of statistical models to study signals, far beyond the more classical class of Gaussian processes. In this framework, signals are represented as realizations of random processes that are soluti ...

2020

Stationary time-vertex signal processing

Nathanaël Perraudin, Andreas Loukas

This paper considers regression tasks involving high-dimensional multivariate processes whose structure is dependent on some known graph topology. We put forth a new definition of time-vertex wide-sense stationarity, or joint stationarity for short, that g ...

2019

Extremal behaviour of aggregated data with an application to downscaling

Sebastian Engelke, Raphaël Gérard Théodore Michel Marie de Deloÿe et Fourcade de Fondeville

The distribution of spatially aggregated data from a stochastic process may exhibit tail behaviour different from that of its marginal distributions. For a large class of aggregating functionals we introduce the -extremal coefficient, which quantifies this ...

OXFORD UNIV PRESS2019

Scaling Limits of Solutions of Linear Stochastic Differential Equations Driven by Levy White Noises

Michaël Unser, Julien René Fageot

Consider a random process s that is a solution of the stochastic differential equation Ls = w with L a homogeneous operator and w a multidimensional Levy white noise. In this paper, we study the asymptotic effect of zooming in or zooming out of the process ...

2019

Diffusion Learning In Non-Convex Environments

Ali H. Sayed, Stefan Vlaski

Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, recent years have seen rising interest in the behavior of gradient-descent based algorithms in non-convex environments. Most of the works on d ...

IEEE2019

Path properties of the solution to the stochastic heat equation with Levy noise

Robert Dalang, Carsten Hao Ye Chong, Thomas Marie Jean-Baptiste Humeau

We consider sample path properties of the solution to the stochastic heat equation, in Rd or bounded domains of Rd, driven by a Levy space-time white noise. When viewed as a stochastic process in time with values in an infinite-dimensional space, the solut ...

SPRINGER2019

Application of Time Series Methods on Long-Term Structural Monitoring Data for Fatigue Analysis

Eugen Brühwiler, Bartlomiej Wojciech Sawicki

Structural health monitoring (SHM) can be employed to reduce uncertainties in different aspects of structural analysis such as: load modeling, crack development, corrosion rates, etc. Fatigue is one of the main degradation processes of structures that caus ...

2019

The Decision Rule Approach to Optimisation under Uncertainty: Methodology and Applications

Daniel Kuhn, Wolfram Wiesemann

Dynamic decision-making under uncertainty has a long and distinguished history in operations research. Due to the curse of dimensionality, solution schemes that naively partition or discretize the support of the random problem parameters are limited to sma ...

2019

The asymmetric multitype contact process

Thomas Mountford, Daniel Rodrigues Valesin

We study the multitype contact process on Z(d) under the assumption that one of the types has a birth rate that is larger than that of the other type, and larger than the critical value of the standard contact process. We prove that, if initially present, ...

ELSEVIER SCIENCE BV2019

A Physical Model of Non-stationary Blur in Ultrasound Imaging

Jean-Philippe Thiran, Yves Wiaux, Paul Hurley, Marcel Arditi, Matthieu Martin Jean-André Simeoni, Adrien Georges Jean Besson, Dimitris Perdios

Conventional ultrasound (US) imaging relies on delay-and-sum (DAS) beamforming which retrieves a radio- frequency (RF) image, a blurred estimate of the tissue reflectivity function (TRF). Despite the non-stationarity of the blur induced by propagation effe ...

2019

Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems

Michaël Unser, Julien René Fageot, Anaïs Laure Marie-Thérèse Badoual

This paper deals with the resolution of inverse problems in a periodic setting or, in other terms, the reconstruction of periodic continuous-domain signals from their noisy measurements. We focus on two reconstruction paradigms: variational and statistical ...

2018